This is a long post, but the OP asked what to look out for, and I've seen a bunch of these trucks.
The earlier 4.0L SOHC engines had timing chain tensioner issues, along with a couple other Ford engines of the same vintage. This issue had been resolved by 2006. Timing chain replacement on this engine is still a royal pain, but if the truck is believed to have 80k miles it should not be an issue for a long, long time. Change the oil at regular intervals using a 5W or 10W-30 of your choice and they live a long life.
These engines have a plastic thermostat housing, which WILL leak, and will eventually fail if not addressed. They are not at all difficult nor expensive to replace, if you are on this forum you probably have the skill to replace it in your driveway in under an hour. If it is not leaking after 16 years and 80k miles, it had probably been replaced at least once already. Give it a cursory glance whenever you do maintenance.
If it has an electric-shifting transfer case, you will want to cycle it a few times to verify it works consistently. The motors tend to stick up if they are not cycled regularly. It should shift immediately between 2 high and 4 high at any speed, when shifting into low range the truck must be completely stopped, in neutral with the brake pedal depressed.
The 5R55E automatic used in '98-'11 4.0L SOHC Rangers got a bad reputation from the earlier models, which had a tendency to blow out the valve body gasket, often causing major issues in reverse, first, and shifting up and down. There was a TSB out to address this issue, but many of them burned up before they got fixed. After the 2002 model year this was no longer an issue on new trucks, but you will want to make sure the fluid is changed regularly. I stick to 30k. This transmission is very picky on fluid, Mercon V is the only suitable choice. If the fluid looks clean and it feels strong in first and reverse, you are good. An auxiliary transmission cooler will help, if the truck does not already have one. Best $60 you will ever spend.
I would pull the plug and check the level and condition of fluid in the differentials. If the rear is supposed to be limited slip, see how it reacts around a tight corner. Check for slop in the bearings if you can.
Check the frame for rust, especially behind the rear spring mounts, even if the body does not have any rust. Once you see one with no metal left back there, you will understand.
Check the ball joints, too. At 80k miles and being a 4x4, they may well need replaced soon, depending on how it has been driven. I have seen some of these trucks on their third set by 70k and some at 250k on the originals.
At some point while DD'ing it you will probably see water leak inside the cab through the rear window, third brake light, and cowl vent. These are fairly simple to address, when you get into it. These issues and fixes are well documented on all the Ranger forums.